Nonlinear Matroid Optimization and Experimental Design

Copyright © [2008] by The Society for Industrial and Applied Mathematics. All rights reserved

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids.

Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail.

By: Yael Berstein; Jon Lee; Hugo Maruri-Aguilar; Shmuel Onn; Eva Riccomagno; Robert Weismantel; Henry Wynn

Published in: SIAM Journal on Discrete Mathematics, volume 22, (no 3), pages 901-919 in 2008


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